Coin Change 2

Description

You are given coins of different denominations and a total amount of money. Write a function to compute the number of combinations that make up that amount. You may assume that you have infinite number of each kind of coin.

 

Example 1:

Input: amount = 5, coins = [1, 2, 5]
Output: 4
Explanation: there are four ways to make up the amount:
5=5
5=2+2+1
5=2+1+1+1
5=1+1+1+1+1

Example 2:

Input: amount = 3, coins = [2]
Output: 0
Explanation: the amount of 3 cannot be made up just with coins of 2.

Example 3:

Input: amount = 10, coins = [10] 
Output: 1

 

Note:

You can assume that

• 0 <= amount <= 5000
• 1 <= coin <= 5000
• the number of coins is less than 500
• the answer is guaranteed to fit into signed 32-bit integer

Solution(javascript)

// // Recursive with memo
// const change = (n, coins) => {
//   const arr = coins
//   const memo = {}
//   const aux = (index = 0, amount = 0) => {
//     memo[index] = memo[index] || {}
//     if (memo[index][amount] !== undefined) {
//       return memo[index][amount]
//     }
//     if (amount === n) {
//       return 1
//     }
//     if (amount > n || index >= arr.length) {
//       return 0
//     }
//     memo[index][amount] = aux(index, amount + arr[index]) + aux(index + 1, amount)
//     return memo[index][amount]
//   }
//   return aux()
// }


// 2: Bottom-up
const change = (n, coins) => {
  if (!coins.length) {
    return n === 0
  }
  const arr = coins
  let memo = []
  for (let i = arr.length - 1; i >= 0; i--) {
    const current = []
    for (let amount = n; amount >= 0; amount--) {
      if (amount === n) {
        current[amount] = 1
      } else {
        current[amount] = (current[amount + arr[i]] || 0) + (memo[amount] || 0)
      }
    }
    memo = current
  }
  return memo[0]
}